Geometry formulas
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This document contains formulas for calculating properties of common geometric shapes such as triangles, rectangles, circles, spheres, and coordinate geometry. It includes formulas for: - Calculating the perimeter, area, and properties of triangles like the Pythagorean theorem - Calculating the perimeter, area, and properties of quadrilaterals like squares, rectangles, parallelograms, and trapezoids - Calculating circumference, arc length, sectors, and properties of circles - Calculating surface area and volume of three-dimensional shapes like cubes, cylinders, cones, and spheres - Calculating distance, midpoints, slopes and the general form of lines in coordinate geometry
![Trapezoid Formula
Perimeter ܤଵ ܤଶ ܵଵ ܵଶ
Area
1
2
ሺ݁ݏܽܤଵ ݁ݏܽܤଶሻ ݐ݄݃݅݁ܪ
Circumference Formula
Circumference #1 ߨ݀
Circumference #2 2ߨݎ
Diameter
ܥ
ߨ
Radius
ܥ
2ߨ
Arc of Circle Formula
Arc Length (Central)
ݏ݁݁ݎ݃݁ܦ ݂ ݈ܽݎݐ݊݁ܥ ݈݁݃݊ܣ
360º
ܥ
Arc Length (Inscribed)
2 ݏ݁݁ݎ݃݁ܦ ݂ ܾ݀݁݅ݎܿݏ݊ܫ ݈݁݃݊ܣ
360º
ܥ
Arc of Circle Formula
Arc Measure (Intersecting Chords) [1] ൏ ܲ ൌ൏ ܳ ൌ
ܥܣ ܦܤ
2
Arc Measure (Intersecting
Secants/Tangents) [2] ൏ ܥ ൌ
ܦܣ ܦܤ
2
Perimeter of Sector of Circle Arc Measure + 2r
A
C
D
B
P Q
A
B
C
D
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Geometry formulas
- 1. Geometry Formulas Triangle Formula Pythagorean Theorem ܽଶ ܾଶ ൌ ܿଶ 45º-45º-90º Phenomenon :ݔ :ݔ 2√ݔ h=2√ݔ 30º-60º-90º Phenomenon ܾ ൌ 3√ݔ :ݔ :3√ݔ 2ݔ Perimeter s1+s2+s3 Area of any Triangle 1 2 ሺܪܤሻ Area of Isosceles Triangle 1 2 ሺ݈݁݃ሻଶ Area of Right Triangle 1 2 ሺܮଵ ܮଶሻ Area of Equilateral Triangle ݏଶ √3 4 Square Formula Perimeter 4S Area #1 S2 Area #2 1 2ൗ ݈ܽ݊݃ܽ݅ܦଶ Relationship between Side & Diagonal ܵ ൌ ܦ √2 D = S2 Rectangle Formula Perimeter 2ሺܮ ܹሻ Area #1 ܮ ܹ Relationship between Side & Diagonal ݄ݐ݃݊݁ܮଶ ܹ݄݅݀ݐଶ ൌ ݈ܽ݊݃ܽ݅ܦଶ Parallelogram Formula Perimeter 2ሺܮ ܹሻ Area ܤ ܪ Rhombus Formula Perimeter 4ܵ Area #1 ܤ ܪ Area #2 1 2 ሺ݀ଵ ݀ଶሻ
- 2. Trapezoid Formula Perimeter ܤଵ ܤଶ ܵଵ ܵଶ Area 1 2 ሺ݁ݏܽܤଵ ݁ݏܽܤଶሻ ݐ݄݃݅݁ܪ Circumference Formula Circumference #1 ߨ݀ Circumference #2 2ߨݎ Diameter ܥ ߨ Radius ܥ 2ߨ Arc of Circle Formula Arc Length (Central) ݏ݁݁ݎ݃݁ܦ ݂ ݈ܽݎݐ݊݁ܥ ݈݁݃݊ܣ 360º ܥ Arc Length (Inscribed) 2 ݏ݁݁ݎ݃݁ܦ ݂ ܾ݀݁݅ݎܿݏ݊ܫ ݈݁݃݊ܣ 360º ܥ Arc of Circle Formula Arc Measure (Intersecting Chords) [1] ൏ ܲ ൌ൏ ܳ ൌ ܥܣ ܦܤ 2 Arc Measure (Intersecting Secants/Tangents) [2] ൏ ܥ ൌ ܦܣ ܦܤ 2 Perimeter of Sector of Circle Arc Measure + 2r A C D B P Q A B C D 1 2
- 3. Circle Formula Area of Circle #1 ߨݎଶ Area of Circle #2 ߨ ݀ଶ 4 Sector of Circle Formula Area of Sector ݏ݁݁ݎ݃݁ܦ ݂ ݈ܽݎݐ݊݁ܥ ݈݁݃݊ܣ 360º ܽ݁ݎܣ ݈݁ܿݎ݅ܥ Rectangular Solids Formula Area of Front & Back Faces 2ሺ݄ݐ݃݊݁ܮ ݐ݄݃݅݁ܪሻ Area of Top & Bottom Faces 2ሺ݄ݐ݃݊݁ܮ ܹ݄݅݀ݐሻ Area of Front & Back Faces 2ሺܹ݄݅݀ݐ ݐ݄݃݅݁ܪሻ Total Surface 2ሺܪܮ ܹܮ ܹܪሻ Diagonal ܦ ൌ ඥܮଶ ܹଶ ܪଶ Cube Formula Area of Cube 6ܵଶ Volume ܵଷ Diagonal ܦ ൌ ܵ√3 ܵ ൌ ܦ √3 Cylinder Formula Area of Top & Bottom Circular Bases ߨݎଶ ߨݎଶ ൌ 2ߨݎଶ Lateral Surface Area 2ߨ݄ݎ Total Surface Area 2ߨݎଶ 2ߨ݄ݎ Volume ߨݎଶ ݄
- 4. Cone Formula Surface Area ߨ݈ݎ ߨݎଶ Volume of Cone 1 3 ߨݎଶ ݄ 1/3 (area of Cylinder) Sphere Formula Surface Area 4ߨݎଶ Volume 4 3 ߨݎଷ Coordinate geometry Formula Distance ඥሺݔଵ െ ݔଶሻଶ ሺݕଵ െ ݕଶሻଶ Mid-point ሺ ݔଵ ݔଶ 2 , ݕଵ ݕଶ 2 ሻ General Form ݕ ൌ ݉ݔ ܾ Slope ݕଵ െ ݕଶ ݔଵ െ ݔଶ